9 cards are dealt to three people at random, so that everyone gets 3 cards. What is the probability that everyone gets a red card?

Reds(A,B,C)  Blue(A,B,C).  yellow(A,B,C)

 Feb 20, 2022

If we were to randomly arrange the cards such that the first 3 cards would be for the first person and so on, there would be 9! ways to do so.

Now, if we were to distribute the 3 red cards such that each person gets one, there are 6 ways that could happen. Then, we can distribute the remaining 6 cards using the same above method to get 6! ways.

That means the final probability is 6*6!/9!=1/84



 Feb 20, 2022

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